CHAPTER 9: FUNDAMENTALS OF HYPOTHESIS TESTING: ONE …s3.amazonaws.com/prealliance_oneclass_sample/nKDb93GPGa.pdf · 228 Fundamentals of Hypothesis Testing: One-Sample Tests CHAPTER

228 Fundamentals of Hypothesis Testing: One-Sample Tests

CHAPTER 9: FUNDAMENTALS OF HYPOTHESIS TESTING: ONE-SAMPLE TESTS

1. Which of the following would be an appropriate null hypothesis?a) The mean of a population is equal to 55. b) The mean of a sample is equal to 55.c) The mean of a population is greater than 55.d) Only (a) and (c) are true.

ANSWER:aTYPE: MC DIFFICULTY: Easy KEYWORDS: form of hypothesis

2. Which of the following would be an appropriate null hypothesis?a) The population proportion is less than 0.65. b) The sample proportion is less than 0.65.c) The population proportion is no less than 0.65.d) The sample proportion is no less than 0.65.

ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: form of hypothesis

3. Which of the following would be an appropriate alternative hypothesis?a) The mean of a population is equal to 55. b) The mean of a sample is equal to 55.c) The mean of a population is greater than 55.d) The mean of a sample is greater than 55.

ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: form of hypothesis

4. Which of the following would be an appropriate alternative hypothesis?a) The population proportion is less than 0.65. b) The sample proportion is less than 0.65.c) The population proportion is no less than 0.65.d) The sample proportion is no less than 0.65.

ANSWER:aTYPE: MC DIFFICULTY: Easy KEYWORDS: form of hypothesis


5. A Type II error is committed whena) we reject a null hypothesis that is true.b) we don't reject a null hypothesis that is true.c) we reject a null hypothesis that is false.d) we don't reject a null hypothesis that is false.

ANSWER:dTYPE: MC DIFFICULTY: EasyKEYWORDS: type II error

6. A Type I error is committed whena) we reject a null hypothesis that is true.b) we don't reject a null hypothesis that is true.c) we reject a null hypothesis that is false.d) we don't reject a null hypothesis that is false.

ANSWER:aTYPE: MC DIFFICULTY: Easy KEYWORDS: type I error

7. The power of a test is measured by its capability ofa) rejecting a null hypothesis that is true.b) not rejecting a null hypothesis that is true.c) rejecting a null hypothesis that is false.d) not rejecting a null hypothesis that is false.

ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: power

8. If we are performing a two-tailed test of whether µ = 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.

a) less thanb) greater thanc) equal tod) not comparable to

ANSWER:aTYPE: MC DIFFICULTY: Moderate KEYWORDS: power

Fundamentals of Hypothesis Testing: One-Sample Tests 230

9. True or False: For a given level of significance, if the sample size is increased, the power of the test will increase.

ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: power, level of significance, sample size

10. True or False: For a given level of significance, if the sample size is increased, the probability of committing a Type I error will increase.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: level of significance, sample size, type I error

11. True or False: For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: level of significance, sample size, type II error

12. True or False: For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: sample size, type I error, type II error

13. If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000

a) either a one-tailed or two-tailed test could be used with equivalent results.b) a one-tailed test should be utilized.c) a two-tailed test should be utilized.d) none of the above

ANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: one-tailed test


14. If an economist wishes to determine whether there is evidence that average family income in a community equals $25,000

a) either a one-tailed or two-tailed test could be used with equivalent results.b) a one-tailed test should be utilized.c) a two-tailed test should be utilized.d) none of the above

ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: two-tailed test

15. If the p-value is less than α in a two-tailed test,a) the null hypothesis should not be rejected.b) the null hypothesis should be rejected.c) a one-tailed test should be used.d) no conclusion should be reached.

ANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: p-value, level of significance

16. If a test of hypothesis has a Type I error probability (α ) of 0.01, we meana) if the null hypothesis is true, we don't reject it 1% of the time.b) if the null hypothesis is true, we reject it 1% of the time.c) if the null hypothesis is false, we don't reject it 1% of the time.d) if the null hypothesis is false, we reject it 1% of the time.

ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: type I error, level of significance

17. If the Type I error (α ) for a given test is to be decreased, then for a fixed sample size na) the Type II error (β ) will also decrease.b) the Type II error (β ) will increase.c) the power of the test will increase.d) a one-tailed test must be utilized.

ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: type I error, type II error, sample size


18. For a given sample size n, if the level of significance (α ) is decreased, the power of the testa) will increase.b) will decrease.c) will remain the same.d) cannot be determined.

ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: level of significance, power, sample size

19. For a given level of significance (α ), if the sample size n is increased, the probability of a Type II error (β )

a) will decrease.b) will increase.c) will remain the same.d) cannot be determined.

ANSWER:aTYPE: MC DIFFICULTY: Moderate KEYWORDS: level of significance, beta risk, sample size

20. If a researcher rejects a true null hypothesis, she has made a _______error.

ANSWER:Type I TYPE: FI DIFFICULTY: Easy KEYWORDS: type I error

21. If a researcher accepts a true null hypothesis, she has made a _______decision.

ANSWER:correct TYPE: FI DIFFICULTY: Easy KEYWORDS: decision

22. If a researcher rejects a false null hypothesis, she has made a _______decision.

ANSWER:correct TYPE: FI DIFFICULTY: Easy KEYWORDS: decision

23. If a researcher accepts a false null hypothesis, she has made a _______error.

ANSWER:Type II TYPE: FI DIFFICULTY: Easy KEYWORDS: type II error

24. It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

a) a two-tailed test for µ is used.


b) a one-tailed test for µ is used.c) Both of the previous statements are true.d) None of the previous statements is true.

ANSWER:aTYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, two-tailed test

25. The power of a statistical test isa) the probability of not rejecting H0 when it is false.b) the probability of rejecting H0 when it is true.c) the probability of not rejecting H0 when it is true.d) the probability of rejecting H0 when it is false.

ANSWER:dTYPE: MC DIFFICULTY: Moderate KEYWORDS: power

26. The symbol for the power of a statistical test isa) α .b) 1 – α .c) β .d) 1 – β .

ANSWER:dTYPE: MC DIFFICULTY: Easy KEYWORDS: power

27. Suppose we wish to test H0: µ ≤ 47 versus H1: µ > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?

a) We have made a Type I error.b) We have made a Type II error.c) We have made a correct decision.d) None of the above are correct.

ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, conclusion


28. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, s = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.

a) H0 : µ ≤ 60 and H1 : µ > 60.b) H0 : µ ≥ 60 and H1 : µ < 60.

c) H0 : X ≥ 60 and H1 : X < 60.

d) H0 : X = 52 and H1 : X ≠ 52.

ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, form of hypothesis, mean, t test

29. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, s = 22. Using the sample information provided, calculate the value of the test statistic.

a) ( )52 60 /22t = −

b) ( ) ( )52 60 / 22/100t = −

c) ( ) ( )252 60 / 22/100t = −

d) ( ) ( )52 60 / 22/10t = −

ANSWER:dTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, mean, t test

30. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, s = 22. Suppose the alternative we wanted to test was H1 : µ < 60 . State the correct rejection region for α = 0.05.

a) Reject H0 if t > 1.6604.b) Reject H0 if t < – 1.6604.c) Reject H0 if t > 1.9842 or Z < – 1.9842.d) Reject H0 if t < – 1.9842.

ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, mean, t test, rejection region


31. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, s = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decisions is correct?

a) At α = 0.05, we do not reject H0.b) At α = 0.05, we reject H0.c) At α = 0.05, we accept H0.d) At α = 0.10, we do not reject H0.

ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, mean, t test, decision

32. How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, s = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following conclusions is correct?

a) At α = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.

b) At α = 0.05, there is sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues.

c) At α = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.

d) At α = 0.10, there is sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.

ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, mean, t test, conclusion

33. We have created a 95% confidence interval for µ with the result (10, 15). What decision will we make if we test H0 : µ =16 versus H1 : µ ≠ 16 at α = 0.05?

a) Reject H0 in favor of H1.b) Accept H0 in favor of H1.c) Fail to reject H0 in favor of H1.d) We cannot tell what our decision will be from the information given.

ANSWER:aTYPE: MC DIFFICULTY: EasyKEYWORDS: two-tailed test, confidence interval, mean, t test, decision




ANSWER:aTYPE: MC DIFFICULTY: DifficultEXPLANATION: The 90% confidence interval is narrower than (10, 15), which still does not contain 16.KEYWORDS: two-tailed test, confidence interval, mean, t test, decision



ANSWER:dTYPE: MC DIFFICULTY: DifficultEXPLANATION: The 97.5% confidence interval is wider than (10, 15), which could have contained 16 or not have contained 16.KEYWORDS: two-tailed test, confidence interval, mean, t test, decision

36. Suppose we want to test H0 : µ ≥ 30 versus H1 : µ < 30 . Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of H1?

a) X = 28, s = 6b) X = 27, s = 4c) X = 32, s = 2d) X = 26, s = 9

ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, rejection region


37. Which of the following statements is NOT true about the level of significance in a hypothesis test?a) The larger the level of significance, the more likely you are to reject the null hypothesis.b) The level of significance is the maximum risk we are willing to accept in making a Type I

error.c) The significance level is also called the α level.d) The significance level is another name for Type II error.

ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: level of significance

38. If, as a result of a hypothesis test, we reject the null hypothesis when it is false, then we have committed

a) a Type II error.b) a Type I error.c) no error.d) an acceptance error.

ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: decision, type I error, type II error

39. The value that separates a rejection region from a non-rejection region is called the _______.

ANSWER:critical valueTYPE: FI DIFFICULTY: EasyKEYWORDS: critical value, rejection region

40. A is a numerical quantity computed from the data of a sample and is used to reach a decision on whether or not to reject the null hypothesis.

a) significance levelb) critical valuec) test statisticd) parameter

ANSWER:cTYPE: MC DIFFICULTY: EasyKEYWORDS: test statistic


41. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are:

a) H0 : µ ≥ 30 versus H1 : µ < 30 .b) H0 : µ ≤ 30 versus H1 : µ > 30 .

c) H0 : X ≥ 30 versus H1 : X < 30 .

d) H0 : X ≤ 30 versus H1 : X > 30 .

ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, form of hypothesis, form of hypothesis, mean

42. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to be 99% confident in her decision, what rejection region should she use?

a) Reject H0 if t < – 2.34.b) Reject H0 if t < – 2.55.c) Reject H0 if t > 2.34.d) Reject H0 if t > 2.58.

ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, mean, Z test, t test, rejection region

43. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what decision should she make?

a) Reject H0.b) Accept H0.c) Fail to reject H0.d) We cannot tell what her decision should be from the information given.

ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, mean, t test, decision


44. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to be 99% confident in her decision, what conclusion can she make?

a) There is not sufficient evidence that the mean age of her customers is over 30.b) There is sufficient evidence that the mean age of her customers is over 30.c) There is not sufficient evidence that the mean age of her customers is not over 30.d) There is sufficient evidence that the mean age of her customers is not over 30.

ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, mean, t test, conclusion

45. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p-value associated with the test statistic?

a) 0.3577b) 0.1423c) 0.0780d) 0.02

ANSWER:cTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, mean, t test, p-value

46. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:

a) – 4.12.b) – 2.33.c) – 1.86.d) – 0.07.

ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, proportion, test statistic


47. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose that the test statistic is – 2.20. Can we conclude that H0 should be rejected at the (a) α = 0.10, (b) α = 0.05, and (c) α = 0.01 level of Type I error?

a) (a) yes; (b) yes; (c) yesb) (a) no; (b) no; (c) noc) (a) no; (b) no; (c) yesd) (a) yes; (b) yes; (c) no

ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, proportion, decision

48. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose you reject the null hypothesis. What conclusion can you draw?

a) There is not sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.

b) There is sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90.

c) There is not sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.

d) There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.

ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: one-tailed test, proportion, conclusion

49. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. State the test of interest to the rental chain.

a) H0 : p ≤ 0.32 versus H1 : p > 0.32b) H0 : p ≤ 0.25 versus H1 : p > 0.25c) H0 : p ≤ 5,000 versus H1 : p > 5,000d) H0 : µ ≤ 5,000 versus H1 : µ > 5,000

ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, proportion, form of hypothesis, form of hypothesis


50. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The value of the test statistic in this problem is approximately equal to:

a) 2.80.b) 2.60.c) 1.94.d) 1.30.

ANSWER:aTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, proportion, Z test, test statistic

51. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The p-value associated with the test statistic in this problem is approximately equal to:

a) 0.0100.b) 0.0051.c) 0.0026.d) 0.0013.

ANSWER:cTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, proportion, Z test, p-value

52. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The decision on the hypothesis test using a 3% level of significance is:

a) to reject H0 in favor of H1.b) to accept H0 in favor of H1.c) to fail to reject H0 in favor of H1.d) We cannot tell what the decision should be from the information given.

ANSWER:aTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, proportion, Z test, decision


53. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The rental chain's conclusion from the hypothesis test using a 3% level of significance is:

a) to open a new store.b) not to open a new store.c) to delay opening a new store until additional evidence is collected.d) We cannot tell what the decision should be from the information given.

ANSWER:aTYPE: MC DIFFICULTY: EasyKEYWORDS: one-tailed test, proportion, Z test, conclusion

54. An entrepreneur is considering the purchase of a coin-operated laundry. The present owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals a daily average revenue of $625. If you were to test the null hypothesis that the daily average revenue was $675, which test would you use?

a) Z-test of a population meanb) Z-test of a population proportionc) t test of a population meand) 2χ -test of population variance

ANSWER:aTYPE: MC DIFFICULTY: ModerateKEYWORDS: two-tailed test, mean, Z test

55. An entrepreneur is considering the purchase of a coin-operated laundry. The present owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals a daily average revenue of $625. If you were to test the null hypothesis that the daily average revenue was $675 and decide not to reject the null hypothesis, what can you conclude?

a) There is not enough evidence to conclude that the daily average revenue was $675.b) There is not enough evidence to conclude that the daily average revenue was not $675.c) There is enough evidence to conclude that the daily average revenue was $675.d) There is enough evidence to conclude that the daily average revenue was not $675.

ANSWER:bTYPE: MC DIFFICULTY: ModerateKEYWORDS: two-tailed test, mean, Z test, conclusion


56. A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you wanted to test whether the auditor should conclude that there is evidence that the average balance is different from $75, which test would you use?

a) Z-test of a population meanb) Z-test of a population proportionc) t test of population meand) χ 2 -test of population variance

ANSWER:cTYPE: MC DIFFICULTY: EasyKEYWORDS: two-tailed test, mean, t test

57. A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you wanted to test whether the average balance is different from $75 and decided to reject the null hypothesis, what conclusion could you draw?

a) There is not evidence that the average balance is $75.b) There is not evidence that the average balance is not $75.c) There is evidence that the average balance is $75.d) There is evidence that the average balance is not $75.

ANSWER:dTYPE: MC DIFFICULTY: moderateKEYWORDS: two-tailed test, mean, t test, conclusion

58. The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact car owners is selected and 79 indicate that they would have purchased the inflatable air bag. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?

a) Z-test of a population meanb) Z-test of a population proportionc) t test of population meand) χ 2 -test of population variance

ANSWER:bTYPE: MC DIFFICULTY: EasyKEYWORDS: two-tailed test, proportion


59. The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact car owners is selected and 79 indicate that they would have purchased the inflatable air bag. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not to reject the null hypothesis, what conclusion could you draw?

a) There is sufficient evidence that the proportion is 0.30.b) There is not sufficient evidence that the proportion is 0.30.c) There is sufficient evidence that the proportion is 0.30.d) There is not sufficient evidence that the proportion is not 0.30.

ANSWER:dTYPE: MC DIFFICULTY: EasyKEYWORDS: two-tailed test, proportion, conclusion

TABLE 9-1

Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 20. She will make her decision using a test with a level of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 Monarch butterflies:

n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82; Null Hypothesis: H0 : µ ≤ 20.000 ; α = 0.10; df = 45; T Test Statistic = 2.09;One-Tailed Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.

60. Referring to Table 9-1, the parameter the biologist is interested in is:a) the mean number of butterflies in Pismo Beach State Park.b) the mean number of parasites on these 46 butterflies.c) the mean number of parasites on Monarch butterflies in Pismo Beach State Park.d) the proportion of butterflies with parasites.

ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: mean, t test, parameter

61. Referring to Table 9-1, state the alternative hypothesis for this study.

ANSWER:000.20:1 >µH

TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, t test, form of hypothesis


62. Referring to Table 9-1, what critical value should the biologist use to determine the rejection region?

a) 1.6794b) 1.3006c) 1.3002d) 1.28

ANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, t test, critical value

63. True or False: Referring to Table 9-1, the null hypothesis would be rejected.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, t test, decision

64. True or False: Referring to Table 9-1, the null hypothesis would be rejected if a 4% probability of committing a Type I error is allowed.


65. True or False: Referring to Table 9-1, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, t test, decision

66. Referring to Table 9-1, the lowest probability at which the null hypothesis can be rejected is ______.

ANSWER:0.021TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, t test, p-value

67. True or False: Referring to Table 9-1, this result proves beyond a doubt that the mean number of parasites on butterflies in Pismo Beach State Park is over 20.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, t test, conclusion

68. True of False: Referring to Table 9-1, the biologist can conclude that there is sufficient evidence to show that the average number of parasites per butterfly is over 20 using a level of significance of 0.10.


ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, t test, conclusion

69. True or False: Referring to Table 9-1, the same decision would have been reached if the biologist had selected a level of significance of 0.05.


70. True or False: Referring to Table 9-1, the same decision would have been reached if the biologist had selected a level of significance of 0.01.

ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, t test, decision

71. True or False: Referring to Table 9-1, the value of β is 0.90.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, t test, beta risk

72. True or False: Referring to Table 9-1, if these data were used to perform a two-tailed test, the p-value would be 0.042.

ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, t test, p-value

73. True or False: Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.043. The null hypothesis should be rejected if the chosen level of significance is 0.05.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: mean, t test, p-value, level of significance, decision


74. True or False: Suppose, in testing a hypothesis about a proportion, the p-value is computed to be 0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.

ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: p-value, level of significance, decision

75. True or False: Suppose, in testing a hypothesis about a proportion, the Z test statistic is computed to be 2.04. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tailed test is used.

ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: proportion, Z test, test statistic, critical value, decision

76. True or False: In testing a hypothesis, statements for the null and alternative hypotheses, as well as the selection of the level of significance, should precede the collection and examination of the data.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issues

77. True or False: The test statistic measures how close the computed sample statistic has come to the hypothesized population parameter.

ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: test statistic

78. True or False: The statement of the null hypothesis always contains an equality.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: form of null hypothesis

79. True or False: The larger the p-value, the more likely one is to reject the null hypothesis.

ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: p-value


80. True or False: The smaller the p-value, the stronger the evidence against the null hypothesis.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: p-value

81. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20, versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.05.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, two-tailed test, decision


ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, two-tailed test, decision


ANSWER:TrueTYPE: TF DIFFICULTY: Difficult KEYWORDS: confidence interval, two-tailed test, decision



ANSWER:FalseTYPE: TF DIFFICULTY: DifficultEXPLANATION: We are not sure if 20 will be in the wider confidence interval.KEYWORDS: confidence interval, two-tailed test, decision

85. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20, versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be accepted at a level of significance of 0.02.

ANSWER:FalseTYPE: TF DIFFICULTY: DifficultEXPLANATION: We are not sure if 20 will be in the wider confidence interval. KEYWORDS: confidence interval, two-tailed test, decision

TABLE 9-2

A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that he can correctly identify a business major 87% of the time, while 13% of the time, he mistakenly identifies an agriculture major as a business major. Presented with one person and asked to identify the major of this person (who is either a business or agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major, and the alternative being that the person is an agriculture major.

86. Referring to Table 9-2, what would be a Type I error?a) Saying that the person is a business major when, in fact, the person is a business major.b) Saying that the person is a business major when, in fact, the person is an agriculture

major.c) Saying that the person is an agriculture major when, in fact, the person is a business

major.d) Saying that the person is an agriculture major when, in fact, the person is an agriculture

major.

ANSWER:cTYPE: MC DIFFICULTY: Difficult KEYWORDS: form of hypothesis, form of hypothesis


87. Referring to Table 9-2, what would be a Type II error?a) Saying that the person is a business major when, in fact, the person is a business major.b) Saying that the person is a business major when, in fact, the person is an agriculture

major.c) Saying that the person is an agriculture major when, in fact, the person is a business

major.d) Saying that the person is an agriculture major when, in fact, the person is an agriculture

major.

ANSWER:bTYPE: MC DIFFICULTY: Difficult KEYWORDS: type II error

88. Referring to Table 9-2, what is the “actual level of significance” of the test?a) 0.13b) 0.16c) 0.84d) 0.87

ANSWER:aTYPE: MC DIFFICULTY: Difficult KEYWORDS: level of significance

89. Referring to Table 9-2, what is the “actual confidence coefficient?”a) 0.13b) 0.16c) 0.84d) 0.87

ANSWER:dTYPE: MC DIFFICULTY: Difficult KEYWORDS: confidence coefficient

90. Referring to Table 9-2, what is the value of α ?a) 0.13b) 0.16c) 0.84d) 0.87

ANSWER:aTYPE: MC DIFFICULTY: Difficult KEYWORDS: level of significance


91. Referring to Table 9-2, what is the value of β ? a) 0.13b) 0.16c) 0.84d) 0.87

ANSWER:bTYPE: MC DIFFICULTY: Difficult KEYWORDS: beta risk

92. Referring to Table 9-2, what is the power of the test? a) 0.13b) 0.16c) 0.84d) 0.87

ANSWER:cTYPE: MC DIFFICULTY: Difficult KEYWORDS: power

TABLE 9-3

An appliance manufacturer claims to have developed a compact microwave oven that consumes an average of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an average of 257.3 W.

93. Referring to Table 9-3, the population of interest is a) the power consumption in the 20 microwave ovens.b) the power consumption in all such microwave ovens.c) the mean power consumption in the 20 microwave ovens.d) the mean power consumption in all such microwave ovens.

ANSWER:bTYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test


94. Referring to Table 9-3, the parameter of interest is a) the mean power consumption of the 20 microwave ovens.b) the mean power consumption of all such microwave ovens.c) 250.d) 257.3.

ANSWER:bTYPE: MC DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, Z test, parameter

95. Referring to Table 9-3, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are:

a) 250 : versus250 : 10 ≠= µµ HH

b) 250 : versus250 : 10 <≥ µµ HH

c) 250 : versus250 : 10 >≤ µµ HH

d) 3.257 : versus3.257 : 10 <≥ µµ HH

ANSWER:cTYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test, form of hypothesis

96. Referring to Table 9-3, for a test with a level of significance of 0.05, the critical value would be ________.

ANSWER:Z = 1.645TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test, critical value

97. Referring to Table 9.3, the value of the test statistic is ________.

ANSWER:2.18TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, Z test, test statistic

98. Referring to Table 9-3, the p-value of the test is ________.

ANSWER:0.0148TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test, p-value


99. True or False: Referring to Table 9-3, for this test to be valid, it is necessary that the power consumption for microwave ovens has a normal distribution.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, Z test, assumptions

100. True or False: Referring to Table 9-3, the null hypothesis will be rejected at a 5% level of significance.

ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test, decision

101. True or False: Referring to Table 9-3, the null hypothesis will be rejected at a 1% level of significance.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test, decision

102. True or False: Referring to Table 9-3, the consumer group can conclude that there is enough evidence to prove that the manufacturer’s claim is not true when allowing for a 5% probability of committing a Type I error.

ANSWER:FalseTYPE: TF DIFFICULTY: Difficult KEYWORDS: one-tailed test, mean, Z test, conclusion


TABLE 9-4

A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with an average of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normal with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A hypothesis test will be done to help make the decision.

103. Referring to Table 9-4, the appropriate hypotheses are:a) 4.7 : versus 4.7 : 10 ≠= µµ HH

b) 4.7 : versus 4.7 : 10 >≤ µµ HH

c) 4.7 : versus 4.7 : 10 <≥ µµ HH

d) 4.7 : versus 4.7 : 10 ≤> µµ HH

ANSWER:cTYPE: MC DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, Z test, form of hypothesis

104. Referring to Table 9-4, for a test with a level of significance of 0.10, the critical value would be ________.

ANSWER:-1.28TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, Z test, critical value

105. Referring to Table 9-4, a sample of size 36 results in a sample mean of 7.1. The value of the test statistic is ________.

ANSWER:-1.50TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, Z test, test statistic

106.Referring to Table 9-4, a sample of size 36 results in a sample mean of 7.1. The p-value of the test is ________.

ANSWER:0.0668TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test, p-value


107. True or False: Referring to Table 9-4, a sample of size 36 results in a sample mean of 7.1. The null hypothesis will be rejected with a level of significance of 0.10.

ANSWER:TrueTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test, decision

108. True or False: Referring to Table 9-4, a sample of size 36 results in a sample mean of 7.1. If the level of significance had been chosen as 0.05, the null hypothesis would be rejected.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test, decision

109. True or False: Referring to Table 9-4, a sample of size 36 results in a sample mean of 7.1. If the level of significance had been chosen as 0.05, the company would market the new anesthetic.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, Z test, conclusion

TABLE 9-5

A bank tests the null hypothesis that the mean age of the bank's mortgage holders is less than or equal to 45, versus an alternative that the mean age is greater than 45. They take a sample and calculate a p-value of 0.0202.

110.True or False: Referring to Table 9-5, the null hypothesis would be rejected at a significance level of α = 0.05.

ANSWER:TrueTYPE: TF DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, decision

111.True or False: Referring to Table 9-5, the null hypothesis would be rejected at a significance level of α = 0.01.

ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, decision


112.True or False: Referring to Table 9-5, the bank can conclude that the average age is greater than 45 at a significance level of α = 0.01.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, conclude

113.Referring to Table 9-5, if the same sample was used to test the opposite one-tailed test, what would be this test's p-value?

a) 0.0202b) 0.0404c) 0.9596d) 0.9798

ANSWER:dTYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, p-value

TABLE 9-6

The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tailed test of the null hypothesis that the mean for the stressed oak furniture is 650. The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test.

114. True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.


115. True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.10, the engineer can conclude that the mean amount of force necessary to produce cracks in stressed oak furniture is 650.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, conclusion


116. True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.05, the null hypothesis would be rejected.

ANSWER:FalseTYPE: TF DIFFICULTY: Easy KEYWORDS: one-tailed test, mean, decision

117. True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.05, the engineer can conclude that the mean amount of force necessary to produce cracks in stressed oak furniture is 650.

ANSWER:FalseTYPE: TF DIFFICULTY: Moderate EXPLANATION: The engineer can conclude that there is insufficient evidence to show that the mean amount of force needed is not 650, but cannot conclude that there is evidence to show that the force needed is 650.KEYWORDS: one-tailed test, mean, conclusion

118. True or False: Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. Then, if the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.


119.Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. What would be the p-value of this one-tailed test?

a) 0.040b) 0.160c) 0.840d) 0.960

ANSWER:aTYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, p-value


120.Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650. What would be the p-value of this one-tailed test?

a) 0.040b) 0.160c) 0.840d) 0.960

ANSWER:dTYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tailed test, mean, p-value

121. True or False: Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650. Then, if the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.

ANSWER:FalseTYPE: TF DIFFICULTY: ModerateKEYWORDS: one-tailed test, mean, decision

TABLE 9-7

A filling machine at a local soft drinks company is calibrated to fill the cans at an average amount of 12 fluid ounces and a standard deviation of 0.5 ounces. The company wants to test whether the standard deviation of the amount filled by the machine is indeed 0.5 ounces. A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.

122. Referring to Table 9-7, the parameter of interest in the test is ________.

ANSWER:Population standard deviation or population varianceTYPE: FI DIFFICULTY: EasyKEYWORDS: two-tailed test, variance, parameter

123. Referring to Table 9-7, which is the appropriate test to use?a) Z-test of a population meanb) Z-test of a population proportionc) t test of a population meand) 2χ -test of population variance

ANSWER:dTYPE: MC DIFFICULTY: ModerateKEYWORDS: two-tailed test, variance


124. True or False: Referring to Table 9-7, in order to perform the test, we need to assume that the amount filled by the machine has a normal distribution.

ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: two-tailed test, variance, assumption

125. Referring to Table 9-7, what type of test should be performed?a) lower-tailed testb) upper-tailed testc) two-tailed testd) none of the above

ANSWER:cTYPE: MC DIFFICULTY: EasyKEYWORDS: two-tailed test, variance, form of hypothesis

126. Referring to Table 9-7, what are the lower and upper critical values of the test when allowing for 5% probability of committing a Type I error?

ANSWER:5.6287 and 26.1189TYPE: PR DIFFICULTY: EasyKEYWORDS: two-tailed test, variance, critical value

127. Referring to Table 9-7, what is the value of the test statistic?

ANSWER:25.1384TYPE: PR DIFFICULTY: EasyKEYWORDS: two-tailed test, variance, test statistic

128. True or False: Referring to Table 9-7, the decision is to reject the null hypothesis when using a 5% level of significance.

ANSWER:FalseTYPE: TF DIFFICULTY: EasyKEYWORDS: two-tailed test, variance, decision

129. True or False: Referring to Table 9-7, there is sufficient evidence to conclude that the standard deviation of the amount filled by the machine is not exactly 0.5 ounces when using a 5% level of significance.

ANSWER:FalseTYPE: TF DIFFICULTY: ModerateKEYWORDS: two-tailed test, variance, conclusion

130. True or False: Referring to Table 9-7, the decision is to reject the null hypothesis when using a 10% level of significance.


ANSWER:TrueTYPE: TF DIFFICULTY: EasyKEYWORDS: two-tailed test, variance, decision

131. True or False: Referring to Table 9-7, there is sufficient evidence to conclude that the standard deviation of the amount filled by the machine is not exactly 0.5 ounces when using a 10% level of significance.

ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: two-tailed test, variance, conclusion

132.True or False: Referring to Table 9-7, the p-value of the test is somewhere between 5% and 10%.

ANSWER:TrueTYPE: TF DIFFICULTY: ModerateKEYWORDS: two-tailed test, variance, p-value

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